You decide to play a game with your friend where your friend places a coin under one of three cups. Your friend would then switch the positions of two of the cups several times so that the coin under one of the cups moves with the cup it is under. You would then select the cup that you think the coin is under. If you won, you would receive the coin, but if you lost, you would have to pay.

As the game starts, you realise that you are really tired, and you don't focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:

He put the coin in the rightmost cup at the start.

He switched two of the cups 3 times.

The first time he switched two of the cups, the rightmost one was switched with another.

The second time he switched two of the cups, the rightmost one was not touched.

The third and last time he switched two of the cups, the rightmost one was switched with another.

You don't want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.

Which cup is most likely to hold the coin?

Hint

Write down the possibilities. Remember that there are only three cups, so if the rightmost cup wasn't touched...Hide

If I want to stay online, my iPad won't let me get a piece if paper and a pen to write down possibilities. That's why I got this wrong and why does my iPad keep auto correcting things so I can't do things? But anyway, that was cool. I wish that were mine!

You (whever posted this teaser) said "He switched two of of the cups 3 times." which seems to say "Two of the cups were swapped 3 times." when your solution (and logic validity) leads me to believe you meant "On 3 occasions, he swapped two cups.". If the rightmost cup was swapped and then not swapped, how can he have swapped the same cups three times in only 3 moves?

Loved this teaser
I nailed it and it felt good
I used ABC though to represent the cups

I ended up with 4 possibilities which are

CBA
BAC
ACB
BAC

the probability then of the coin being under the first cup is 1/4 which is also the same with the probability of it being under the second cup. There are two possibilities however for the coin being under the rightmost cup which are the two BAC above. Hence it has the highest probability which is 1/2